data("wage1", package = "wooldridge")

plot(wage ~ educ, data = wage1)

# make it nicer
library(tinyplot)
plt(wage ~ educ, data = wage1,
     col = "red", pch = 21,
     bg = "orange", grid = TRUE,
    main = "wage vs educ",
    xlab = "educ", ylab = "wage")
plt_add(type = "rug", side = 2)

plt(~wage , data = wage1, type = "density")
# nicer
plt(~wage , data = wage1, type = "density",
    lw = 3, col = "red")


# same plot but use log(wage)


plt(log(wage) ~ educ, data = wage1,
    col = "red", pch = 21,
    bg = "orange", grid = TRUE,
    main = "log wage vs educ",
    xlab = "educ", ylab = "log wage")
plt_add(type = "rug", side = 2)

plt(~log(wage) , data = wage1, type = "density",
    lw = 3, col = "red")


# run 3 models
mods = list()
mods[["level-level"]] = lm(wage ~ educ, data = wage1)
mods[["log-level"]] = lm(log(wage) ~ educ, data = wage1)
mods[["log-log"]] = lm(log(wage) ~ log(educ), data = wage1, subset = educ > 0)

modelsummary::modelsummary(mods)

# college tuition nonlinear
x = read.csv("college_tuition_income.csv")

plt(mid_career_pay  ~ out_of_state_tuition, data = x)
plt_add(type = "lm")
plt_add(type=type_loess(), col = "blue")

lm(mid_career_pay  ~ out_of_state_tuition, data = x)
x$pay1000 = x$mid_career_pay / 1000
x$tuition1000 = x$out_of_state_tuition / 1000

lm(pay1000  ~ tuition1000, data = x)
# dividing LHS and RHS by the same number does not change anything!

m = lm(pay1000  ~ tuition1000 + I(tuition1000^2), data = x)

# predicted pay1000 for tuition1000 = 20?
# a + bx + c x^2
83.76988 -0.33810 * 20 + 0.01692 * 20^2

# predicted pay1000 for tuition1000 = 10,20,30,40?

nd = data.frame(tuition1000 = c(10:50))
nd$prediction = predict(m , newdata = nd)
plt(prediction ~  tuition1000, data = nd, type = "l")